Game Theory Paradox Explained: Losing Strategy that Wins

Do you think playing two losing games can result in a win streak? Parrando’s paradox proves this can happen in a very simple way.

The paradox is illustrated by two games played with coins weighted on one side so that they will not fall evenly by chance to heads or tails.

In game A, a player tosses a single loaded coin and bets on each throw. The probability of winning is less than half. In game B, a player tosses one of two loaded coins with a simple rule added. He plays Coin 1 if his money is a multiple of a particular whole number, like three.

If his money cannot be divided by the number three, he plays the Coin 2. In this setup, the second will be played more often than the first.

Both are loaded, one to lose badly and one to win slightly, with the upshot being that anyone playing this game will eventually lose all his money.

“Sure enough,” Dr. Abbott said, when a person plays either game 100 times, all money taken to the gambling table is lost. But when the games are alternated — playing A twice and B twice for 100 times — money is not lost.

It accumulates into big winnings. Even more surprising, he said, when game A and B are played randomly, with no order in the alternating sequence, winnings also go up and up.

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